In general Bayes procedures offer a tradeoff between bias and variance reduction of the estimates. Particularly in cases where the sample size is small, they produce a set of point estimates that have good properties in terms of minimizing squared error loss (Carlin and Louis 2000). This variance reduction is attained through borrowing information resulting from the adopted hierarchical structure, leading to Bayes point estimates shrunk toward a value related to the distribution of all the units included in the hierarchical structure. The effect of shrinkage is thus dependent on the prior structure that has been assumed and conditional on the latter being close to the true model in some sense. Consequently, different prior structures will lead to different shrinkage. Note that the desirable properties of the estimates thus obtained will depend on the ultimate goal of the estimation exercise. If producing a set of point estimates of the relative risk is the aim, then posterior means of the relative risk are best in squared error loss terms. However, if the goal is to estimate the histogram or the ranks of the area relative risks, different loss function should be considered. The desirability and difficulty of simultaneously achieving these triple goals has been discussed by Shen and Louis (1998) and has been illustrated in spatial case studies by Conlon and Louis (1999) and Stern and Cressie (1999). In our study, we focus on the goal of estimating the overall spatial pattern of risk, which involves producing and interpreting a set of point estimates that will not only give a good indication of the presence of heterogeneity in the relative risks but also highlight where on the map this heterogeneity arises and whether this is linked to isolated high- and/or low-risk areas or to more general spatial aggregation of areas of similar high or low risk. Inference about the latter will depend on the sensitivity and specificity of the posterior risk estimates, as discussed in this article. If the goal is purely the testing of heterogeneity, other methods could be used, such as the Potthoff-Whittinghill test or scan statistics [see Wakefield et al. (2000) for review] that test for particular prespecified patterns of overdispersion. Conversely, if the aim is a local study around a point source, then again, the disease-mapping framework is not appropriate, and focused models that make use of the additional information about the location of the putative cluster of high risk are required (Morris and Wakefield 2000).